The controversial appointment has so far brought in only QPR loanee Loic Remy, who is injured for Saturday's clash at St James' Park, and supporters are unhappy with the role of Kinnear, who is expected to be at the game.
Allardyce said: "I was very surprised when they appointed Joe. He obviously built up a good relationship with the owner the first time he was there. I know Joe has a huge amount of experience (but) he could have made life easier for himself if he had not made the public statements he made. Football clubs are run by the owners. It's their responsibility and they're quite within their right to do what they see fit, i.e. sack me. I wasn't his choice.
"I had a director of football at my first job at Blackpool, Billy Bingham, but I think it depends on the relationship you have or you build. It also depends on the relationship between you, the owner and the director of football.
"If that is working in your favour then that can help the football club, help the results and help you. If not - if the director of football is not promoting the players that you want to buy but the players he wants - it's a massive problem.
"There can be Chinese whispers behind your back. If you start getting that scenario the director of football becomes a bigger obstacle than a help."
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